# The two-phase issue in the O(n) non-linear $\sigma$-model: A Monte Carlo study

## TL;DR

This study uses high-statistics Monte Carlo simulations to examine the phase structure of two-dimensional O(n) non-linear sigma models, providing evidence supporting asymptotic freedom in the O(8) case.

## Contribution

It offers new high-precision Monte Carlo data on the mass gap and susceptibility, clarifying the phase behavior of O(n) models and supporting the asymptotic freedom hypothesis.

## Key findings

- Results support asymptotic freedom in O(8) model
- No evidence of Kosterlitz-Thouless transition observed
- Provides high-precision data for mass gap and susceptibility

## Abstract

We have performed a high statistics Monte Carlo simulation to investigate whether the two-dimensional O(n) non-linear sigma models are asymptotically free or they show a Kosterlitz- Thouless-like phase transition. We have calculated the mass gap and the magnetic susceptibility in the O(8) model with standard action and the O(3) model with Symanzik action. Our results for O(8) support the asymptotic freedom scenario.